You can full-attack invisibly as a Ninja (Complete Adventurer or Dragon Magazine #318, April 2004) with Ghost Step, since it renders you invisible for a full round (it does not duplicate the Invisibility spell so it does not have that spell's restriction; also, Greater Invisibility does not turn you visible after an attack, so an ally casting GI on you can thus allow you to sneak attack with every attack during a flurry of blows).
One wierd build that might be viable is to start as a rogue, go rogue 3, ninja 2, then swordsage 2, followed by monk levels (Before that, rely on weapons as normal, and light armor until you become a ninja). Works best as a human, otherwise you'll take multiclassing penalties most likely.
Rogue 3 and Ninja 2 will give you 2d6 sneak attack and 1d6 sudden strike, plus Wis mod + 1/2 monk level Ki Power uses per day (so Wis mod + 1 Ki Powers/day) along with Ghost Step for invisibility by expending Ki Power uses. Swordsage will give you a few useful stances and maneuvers; when your character level is 4 or higher and you take a level of Swordsage, you'll have an effective initiator level of 3 (your swordsage level + half your other levels) and qualify for the 2nd-level maneuver Cloak of Deception, which is invisibility until the end of your turn when used, and you can use it once per battle at least. So that will allow some more full-attack sneak attack sudden strikes (plus flurry of blows during that when you become a monk later).
Also, the swordsage's Discipline Focus, if applied to Shadow Hand as it should be at 1st-level, will give you Weapon Focus in all Shadow Hand associated weapons, which includes Unarmed Strike. So it can help you qualify for Ring the Golden Bell if you want to take that feat later. Swordsage maneuvers you might also want to take include Shadow Jaunt, Emerald Razor, Fire Riposte, Burning Brand, Burning Blade, and Moment of Perfect Mind (since you'll need at least one Diamond Mind maneuver to qualify for Emerald Razor). Most of these are 2nd-level maneuvers so you can only get them all if you're 4th-level before taking your 1st level in Swordsage. Stance-wise you may want Island of Blades (makes it easier to flank enemies) and either Flame's Blessing, Step of the Wind, or Stance of Clarity.
At 6th-level you could take the Shadow Blade feat, making use of your Shadow Hand stances to deal extra damage equal to your Dexterity bonus with Shadow Hand weapons. At 9th-level or later you could take the Martial Stance feat for an extra stance known, that being Assassin's Stance, which is 3rd-level and requires having some Shadow Hand maneuvers beforehand (you won't qualify for 3rd-level stances or maneuvers until your 8th character level due to the multiclassing). At later levels, you might consider taking Martial Study or Martial Stance for more useful stuff. You might possibly find the Gloom Razor feat useful, but I dunno with this build. And definitely take the Superior Unarmed Strike feat from ToB once you qualify for it, to boost your unarmed damage as though you were a monk 4 levels higher than your actual monk level (probably as your 12th-level feat, since Martial Stance - Assassin's Stance is a better choice at 9th-level, given that it will boost your Sneak Attack by +2d6 when in that stance).
Swordsage and the aforementioned feats, maneuvers, and stances are from Tome of Battle: The Book of Nine Swords. You might also consider the Vexing Flanker feat from Player's Handbook II, if you take Combat Reflexes early on to meet its prerequisite, since your attack bonus won't be as great as a pure rogue or pure monk. Catching opponents with flanking or invisibility msot of the time, however, will at least give you a fair chance of hitting.